3 mins tempo every other day to regain fitness?

Not sure about your potential, but 3-6 months of that should get you much of the way back to the endurance you had six months ago.

Speed helps for a 5k, but general aerobic capacity helps even more. If you genuinely "lost all your endurance" you should probably just steadily build up base mileage for a couple months at least

Thanks. I think I'll start with 5 miles easy each day and then add in the alternating tempo runs

Doing this for a while should give me a very decent base

I would not alternate tempo days, doing 3-4 workouts/week. I would take 3-6 months & build a proper base. 1-2 months of mileage without workouts. Strides are fine. Then you really just need 1 tempo/threshold workout/week. You can add in another workout every other week but I wouldn't start doing a tempo run every other day. Do a mix of mileage. Do a long run, getting up to an hour, & then building from there to 70-80-90min. Do a medium long run where you build from 45-50min to 60+. Then do a lot of 5 mile runs around that. Your workout day should jump up to that 45-50min >>> 60min range. It doesn't have to be a 3 mile tempo. 3-5 miles straight or broken works fine.

Start with easy jogging, like jog for 2 minutes, walk for 1 minute. Repeat. Your muscles and joints will be very prone to injury in the early stages.

Then SLOWLY work up to 2-3 hours of shuffling a week.

When it comes to workouts, always break it up into reps. Tempo runs are stupid.

I’d do the tempo every third day, so two days break between each one, and I would vary the tempo work. One day could be the 3 mile tempo, another can be threshold intervals like 8x800m with short rest, and the next could be a 5-6 mile steady state run (not quite tempo pace but high effort, maybe 10ish seconds slower than half marathon pace if the half marathon pace is based off of your current mile-5k ability)

Dude a 5k is 90% aerobic if not more, especially in this context. Speed aint getting you anywhere except to the back fast.

One of the accepted facts in distance training is that a hard day should be followed by an easy day. If you do 5 miles every day, you're not optimizing your training. A better approach might be 7 and 4 or 6 and 3. Don't do the same mileage every day.

A tempo run every other day is also not optimal.

Your schedule should follow a hard day with an easy day. Here's an example.... Long intervals (600-1200), easy day, tempo or modified tempo, easy day, long run (longer than your easy days... 60-75 minutes). Then repeat on a 6-day or 7-day cycle. If you must fit this into a 7-day cycle, then add another easy day, cross training day, or day off.

If you're flexible, go with the 6-day cycle and when you feel unusually tired or sluggish one day... and that will happen.... abort the workout that day and try it again the next day.

Once in a while, maybe every 2-3 weeks, replace the tempo or interval day with a hill rep day (30-45 seconds) to keep some of your speed.

Eventually, you'll need to advance to workouts based on your goal 5k race pace.

That is silly. Many high school runners do nothing all summer. They show up first day of practice. They run 4 miles per day for 4 days and then start workouts twice per week.

Good runners take 2 weeks off and start back up mid to late June. They do 4 weeks of base work and then add workouts.

Not always. Another pattern is intervals Tuesday, tempo Wednesday, race Saturday.

The OP proposed a schedule that is elegant in its simplicity and appropriate to his goals.

What you have written here is simply overthinking things.

There is no reason to wait 1-2 months before doing simple tempos. (This is a bad idea for an 800 type who should stay in touch with some amount of speed.)

I do agree with you that he should through in strides on the easy days, and that the tempos can be broken up with short rest as 3xMile, 5x1km, etc.

You can't make up fitness, you can only gain it.